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Differentiability of the speed of biased random walks on Galton-Watson trees

Hold Date
2019-10-25 16:30〜2019-10-25 18:00
Seminar Room W1-D-725, West Zone 1, Ito campus, Kyushu University
Object person
researchers and graduate students 
Yuki TOKUSHIGE (Kyoto University)

We prove that the speed of a \lambda-biased random walk on a supercritical Galton-Watson tree is differentiable for \lambda such that the walk is ballistic and obeys a central limit theorem, and give an expression of the derivative using a certain 2-dimensional Gaussian random variable. The proof heavily uses the renewal structure of Galton-Watson trees that was introduced by Lyons-Pemantle-Peres. This talk is based on the joint work with Adam Bowditch (National University of Singapore).